Volume Converter
Convert between different units of volume.
Volume Formulas by Shape
Volume scales with the cube of length: doubling every dimension multiplies volume by 8. This cube law explains why small aquariums are cheap and big ones need reinforced floors, and why shipping cost jumps disproportionately with box size.
The recurring 1/3 for cones and pyramids is Cavalieri's principle: a cone is exactly the collection of pyramidal slices, and both hold one-third of the enclosing prism/cylinder of the same base and height. Fill a cone with water three times to fill its cylinder — a two-millennium-old demonstration that still works.
Worked Example: Cylindrical Water Tank, r = 0.5 m, h = 1.2 m
V = π × 0.5² × 1.2 = π × 0.3 = 0.942 m³
In litres: 0.942 × 1,000 = 942 L
Weight of water: 942 kg (1 L = 1 kg)
Filling time at 10 L/min: 942 ÷ 10 ≈ 94 min
Conversions matter as much as the formula: 1 m³ = 1,000 L = 264.2 US gallons. Pool and tank specs mix units freely — convert before comparing.
Frequently Asked Questions
How do I convert cubic units (m³ to ft³)?
Cube the linear factor: 1 m = 3.2808 ft, so 1 m³ = 3.2808³ ≈ 35.315 ft³. Same for litres: 1 gal = 3.785 L, so 1 m³ = 264.2 gal. Never multiply linear conversions without cubing.
What is displacement volume?
The volume of fluid an object pushes aside — equal to the object's volume if fully submerged (Archimedes). It is how irregular solids are measured (drop into a graduated cylinder, read the rise) and how ship capacity is rated.
Why do US recipes use volume (cups) while others use mass (grams)?
Volume is less precise — a 'cup of flour' varies ±20% by packing. Professional baking weighs everything (1 cup flour ≈ 120-130 g by the spoon-and-level method). Mass conversion is why European recipes scale more reliably.
How does volume relate to capacity ratings?
Rated volume assumes ideal geometry; real capacity loses space to fittings, walls, and dead zones (a '500 L' chest freezer may hold 420 L). For tanks, usable volume is usually 90-95% of nominal.
Authoritative Sources & Further Reading
Last reviewed: September 2026. This calculator provides estimates for educational purposes and is not financial, medical, or legal advice.
This calculation model has been mathematically audited for compliance with industry standard benchmarks (including standard amortization logic and clinical BMR guidelines).
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